I think there is some confusion between 2 different effects.
There are the cathode ray pencil straight beams that are the effects of electric field acceleration. Mostly electrons. Nothing to do with magnetic fields.
These have been noticed in the upper solar latitudes.
Then there are flux tubes which are flows of plasma which are the result of potential differences between areas in a plasma that is denser like at the solar equator. These generally are a twisted pair like the flux tube that lives on the day line in the magnetopause.
And the electric field comes from ...
Flux tubes
may contain plasma flows. A flux tube is just a bundle of magnetic field lines B, nothing more nothing less, defined in such a way that a surface perpendicular to the field, which moves along the field lines, shrinks or stretches with the field lines, in such a way that the product BS remains constant. That is a flux tube, which may or may not contain plasma.
If the footpoints get sheared or twisted, then an EMF is generated (see Alfven for example). I have no idea what you mean with "at the solar equator" flux tubes come out all over the sun and mainly in the band with sun spots.
I do not understand what you mean with "a twisted pair" which you say is "living on the day line of the magnetopause". Why a "pair"? I can just have one flux tube, which can get twisted into a rope by current flow through the tube.
So you still not telling us how the tube field is "produced by the current flowing along it."
"We have found in our study of 130 reconnection events that, in general, magnetic reconnection occurs along an extended line across the dayside magnetopause," said Dr. Karlheinz Trattner, Lockheed Martin space plasma physicist at the ATC. "Previously, there was considerable debate concerning the nature of this reconnection line. Some scientists believed that this reconnection line was not continuous across the dayside magnetopause, while others thought it was. The results from this study have resolved this long-standing debate."
So we move from Sun to Earth. What is it that this is supposed to show? The "paired" flux tubes?
(Some more abstracts taken out)
At interfaces between flux tubes and current sheets, instabilities form known as Dicotron Instabilities.
Is this an interface between flux tubes and an interface between current sheets, or an interface between a flux tube and a current sheet.
I rather doubt that the diocotron instability will happen, maybe the Kelvin-Helmholtz instability, as the former can only occur under very special conditions. Which is why one almost never sees this instability discussed in plasma physics books. For one, a charge separation will have had to have taken place.
Flux tubes form parallel and perpendicular magnetic fields by the combined motions of the electrons and the magnetic fields.
I guess this is your way of saying that the current flow in a flux tube creates a toroidal field (which is perpendicular to the guide field). However the current flow cannot create the parallel field. Please show me how you want to do that.
Some of the electrons go straight and are responsible for the right hand rule like a wire(curl).
"electrons are responsible for the right hand rule ..."
See above
Some of the electrons are in a wide orbit and are responsible for the parallel component of the magnetic field in a flux tube like a solenoid.
Why do they go in a "wide orbit" if the guide field still has to be created by these magical electrons? This is just wrong electrodynamics. You want the electrons to gyrate to create a "parallel" magnetic field (parallel to the "electrons that go straight), but in order for them to gyrate, there has to be this parallel field.
Some do the helical motion and are responsible for the shape of the flux tubes.
No, if you put a voltage drop over the flux tube all electrons will move in helical paths, some more wound then others, if we assume a Maxwellian distribution.
Part of the parallel component depends on the location of the current flow.
If its a true Birkeland current its dominated by the field aligned current because the parallel component is doubled by the i.e. earths magnetic field..
Flux tubes are long lived structures that reconnect on a continual basis.
What is that supposed to mean, "part of the parallel component." I guess you mean that the winding of the field depends on where in the flux rope you are.
A Birkeland current is ALWAYS a field aligned current.
Why is "the parallel component doubled by the (and I guess you mean e.g. [for example] instead of i.e. [that is]) Earth's magnetic field?"